Determine the order and degree of the following differential equation. State also whether it is linear or non-linear.
$\frac{d^{2} y}{d x^{2}} + 4 y = 0$ .

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Solution

Consider the following equation,
$\frac{d^{2} y}{d x^{2}} + 4 y = 0$ .

Order: Order of a differential equation is the order of the highest order derivative (also known as differential coefficient) present in the equation

Degree: The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

Linear/Non-linear: If Exponent of the dependent variable and all its differential coefficients in the given equation is more than one, then the differential equation is Non-linear

So from the above equation, we can say that,

Order: $2$
Degree: $1$
Linear/Non-Linear: Linear.

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